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Rouquier's Cocovering Theorem and Well-generated Triangulated Categories

Published online by Cambridge University Press:  01 September 2010

Daniel Murfet
Daniel Murfet
Affiliation:
Hausdorff Center for Mathematics, University of Bonn, Germany, murfet@math.uni-bonn.de
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Abstract

We study cocoverings of triangulated categories, in the sense of Rouquier, and prove that for any regular cardinal α the condition of α-compactness, in the sense of Neeman, is local with respect to such cocoverings. This was established for ordinary compactness by Rouquier. Our result yields a new technique for proving that a given triangulated category is well-generated. As an application we describe the α-compact objects in the unbounded derived category of a quasi-compact and semi-separated scheme.

Keywords

triangulated categorieswell-generated categoriesderived categories

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Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 1 , August 2011 , pp. 31 - 57
Copyright
Copyright © ISOPP 2010

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